Having used Mac OS X Leopard now for just over a week I can safely say I've had a fairly painless experience using software that was released in the Tiger era, though there have been a few gotchas. In case it's useful to someone I'm posting information on some of the applications I've had minor troubles with.
This is by no means an authoritative study, and it is possible that the software problems I've posted here might be a result of my own unique computer configuration or even misunderstanding on my own part, in which case feel free to correct me by posting a comment :).
X11 to me feels like it's exactly the same in Leopard as it was in Tiger; the title bars and bundled apps are exactly the same. I remember reading somewhere that Leopard was going to be bundled with an Xorg distribution instead of XFree86.
Anyway those issues aside, the problem I seem to have is that even though I move the X11.app icon to the Dock from the Utilities folder, whenever I launch an application that uses X11, another identical X11 icon appears at the end of the dock and the first one that I placed there crashes. This has happened on two wipes and reinstalls of Leopard.
The other issue I have is that X11 doesn't respect the space limits imposed by the Apple menu. If you try and move any normal window on OS X above the Apple menu it doesn't work, but X11 apps are more than happy to creep behind the menu which makes them that much harder to grab and bring back down again:
For some reason when I try and launch Inkscape it informs me that I don't have an X11 compatible environment installed and promptly quits. To work around this, I launch X11 first then Inkscape and it works. Pain in the arse though to have to launch two apps just to use one.
The official LastFM client is really spotty for me in Leopard. Just like X11 when I launch LastFM it launches two concurrent versions of it, one of which instantly crashes.
Force quitting the one that's stuffed up leaves the other working just fine though. Just a small pain to have to deal with every time.
The Good News!
With all those issues you'd think I've been having a terrible time in Leopard with third party applications: fortunately the ones that work far outweigh the ones that don't.
This is my current list of apps I've used in Leopard that work just fine: Quicksilver, VMware Fusion (1.0 and 1.1 Beta), Camino (1.5.2 and 1.5.3), Thunderbird (22.214.171.124), iSquint, NeoOffice, VLC, TextMate, Flickr Uploadr, Xee, the MAMP web server, Snitter and Cyberduck.